I have equation $\left(\left(tk\right)^a+\left(tl\right)^a\right)^b$. Can I say $\left(\left(tk\right)^a+\left(tl\right)^a\right)^b$=$\left(t^a\left(k\right)^a+t^a\left(l\right)^a\right)^b$=$\left(t^a\left(\left(k\right)^a+\left(l\right)^a\right)\right)^b$=$t^{ab}\left(\left(k\right)^a+\left(l\right)^a\right)^b$?
I believe so but the online calculators say no, but not why not.
If $a=\frac12$, $t=k=-1$, $(tk)^a=1$ but $t^ak^a = -1$.
However, if you restrict $t$ and $k$ to be nonnegative number, then you can do so.